The uncertainty in time interval is taken 0.1s because the stopwatch we used had a least count of 0.1 s and was digital. Here, uncertainty in temperature is 0.5°C because the least count of the thermometer was 1°C and it was an analog thermometer.
So uncertainty is half the least count. Now, the average temperature was calculated by taking the sum of the four temperature values for a specific time and dividing the sum by 4. The uncertainty in temperature was calculated by finding the difference between the maximum value and the minimum value and then dividing it by 2. Sample Calculations:
1. Average temperature = (27+28+28+27)/4 = 27.5 = 28°C 2. Uncertainty in temperature = (Max-Min)/2 = (28-27)/2 = 0.5 = 1°C Table 2: Table showing average temperature and uncertainty in this average with corresponding time Time/s ± 0.1 s Average temperature/°C Uncertainty in temperature/°C
The relatively low percentage uncertainty and discrepancy show that the experiment was very precise and accurate. This means that both random and systematic errors were very low. However, there is an outlier in the graph, so there was a systematic error for that value of ‘t’. According to the hypothesis, the graph was supposed to be a straight line which passes through the origin. But here, we can see a y-intercept.
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This means that even when the time was zero, there was a certain temperature (23.8°C).
Here, we know that this is the temperature of the water according to the surrounding when the heating process had not started. And the value from the graph (23.8°C) is quite close to the actual observed value during the experiment (26°C).
The range of the y-intercept also includes a value that can be explained with the same explanation.
ERROR EVALUATION
As mentioned above, the low percentage uncertainty and discrepancy shows that the errors are not very significant. The errors are listed below along with improvements. Random errors: 1. Difficulty in measuring temperature – Measuring the temperature while it was rising was a little tricky as both the time and the temperature had to be observed simultaneously. This was, however, made easier by having two people in the team.
2. Temperature of water is not same throughout the beaker – This means that the water heating does not take place uniformly, so the relative position of the heater and the thermometer affects the values of temperature. Using a heater from the bottom and keeping the thermometer at a fixed height from the bottom would reduce this error. 3. Least count of thermometer – The thermometer we used had a least count of 1°C which is quite high. Using a temperature probe would give us more precise values. Systematic errors:
1. Time taken to heat the heater itself – The heater itself took some time to heat up which could be the cause for the outlier in the graph. 2. Heat lost to surroundings – Heat is lost to the atmosphere as well as the beaker while heating. This constantly decreases the amount of energy supplied, resulting in a lower value for ‘c’. Using a calorimeter with a lid would reduce this.
3. The beaker was kept open – This resulted in evaporation of water and, thus, a decrease in the volume of water. This would result in a decrease in the mass and therefore increase the value of ‘c’. Use of a lid to cover the beaker would help control this error. 4. The power of heater was not measured – We assumed the power mentioned in the packaging to be absolutely true and without uncertainties, but this might not be true. If we measured these ourselves, we would also know the uncertainties and therefore, get a more accurate value.
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5. Power of heater changes with change in temperature – A change in temperature results in a change in the resistance of the heating coil and therefore, the power changes as well. 6. Use of tap water – Tap water contains many impurities, which affects water’s specific heat capacity. Using distilled water would help reduce this. 7. Beaker and heater were not cooled down completely after each trial – The beaker and the heater were rinsed a few times very briefly. This means that they were not cooled down properly and therefore, that provided certain energy to the water.
This decreases the value of ‘c’. 8. The volume of water was measured instead of the mass – The density of water was assumed to be 1 gcm-3, which might not be true because of the impurities in tap water. Directly measuring the mass would have given better results. From these, the most significant errors would be the heat lost to the surroundings and the evaporation in the process. Controlling these two would give a more accurate result.
